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What a coincidence! I asked my students this very question the other day — they had some trouble with it, too.

Given this forum's policy on homework, you'll have to justify that your question is not related to homework (for instance, by describing how you need the answer to create a game or other application) before I can give you the answer. If your question really is a homework question, I suggest that you ask your teacher about it — he's the best person you can ask.

Obviously we can't give you the answer, but here are some things you should be thinking about:

What happens if the graph is disconnected?
Can you draw me a connected graph with exactly one vertex of odd degree?
If you're interested, how about one with three such vertices? Five?

Admiral

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Original post by ToohrVyk What a coincidence! I asked my students this very question the other day — they had some trouble with it, too. Given this forum's policy on homework, you'll have to justify that your question is not related to homework (for instance, by describing how you need the answer to create a game or other application) before I can give you the answer. If your question really is a homework question, I suggest that you ask your teacher about it — he's the best person you can ask.

It would be so funny if it were not a coincidence and he/she is one of your students.